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Asymptotic ${H}_{\infty }$ control of singularly perturbed systems with parametric uncertainties. (English) Zbl 0958.93066
Summary: This paper deals with the problem of control of singularly perturbed linear continuous-time systems. The authors’ attention is focused on the design of a composite linear controller based on the slow and fast problems such that both stability and a prescribed ${H}_{\infty }$ performance for the full-order system are achieved. The asymptotic behavior of the composite controller is studied, which is independent of the singular perturbation parameter $\epsilon$ when $\epsilon$ is sufficiently small. Furthermore, the problem of robust control for the above system with parameter uncertainty is also invstigated.
##### MSC:
 93C70 Time-scale analysis and singular perturbations 93B36 ${H}^{\infty }$-control